{"paper":{"title":"Moment estimates for L\\'{e}vy Processes","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gilles Pag\\`es (PMA), Harald Luschgy","submitted_at":"2006-07-12T09:22:01Z","abstract_excerpt":"For real L\\'{e}vy processes $(X\\_t)\\_{t \\geq 0}$ having no Brownian component with Blumenthal-Getoor index $\\beta$, the estimate $\\E \\sup\\_{s \\leq t} | X\\_s - a\\_p s |^p \\leq C\\_p t$ for every $t \\in [0,1]$ and suitable $a\\_p \\in \\R$ has been established by Millar \\cite{MILL} for $\\beta < p \\leq 2$ provided $X\\_1 \\in L^p$. We derive extensions of these estimates to the cases $p > 2$ and $p \\leq\\beta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607282","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}